Answer
$(5,-2)$ is not a solution of the system.
Work Step by Step
An ordered pair is a solution to the system if it satisfies both equatons:
$ \begin{array}{lllll}
4(5)-3(-2) & =26 & .... & (5) & =15-5(-2)\\
20+6 & =26 & & 5 & =15+10\\
26 & -26 & & 5 & =25\\
TRUE & & & FALSE &
\end{array} $
$(5,-2)$ is not a solution of the system.